Optimal multiresolution quantization with error detecting codes for broadcast channels

This paper investigates the design of optimal vector quantization given channel and error statistics by inclusion of cyclic redundancy checks (CRC) into the consideration. Given a broadcast system with multiresolution vector quantization (MRVQ) and error detection availability for each resolution, a closed-form formula for the weighted end-to-end distortion (EED) is first derived under a random index assignment. Based on the closed-form formula, an iterative algorithm is then proposed for designing optimal MRVQ to minimize the EED with CRC. Experiments show that for a wide range of channel error probability, the inclusion of CRC indeed reduces the EED. Finally, the best tradeoff between the number of bits for quantization and those for CRC is also investigated by experiments.